Stochastic Dynamics of a Vortex Loop. Large Scale Stirring Force

Abstract

Stochastic dynamics of a vortex filament obeying local induced approximation equation plus random agitation is investigated by analytical and numerical methods. The character of a stirring force is supposed to be a white noise with spatial correlator concentrated at large distances comparable with size of the loop. Dependence of the spectral function $<{\mathbf{s}}_{\kappa }^{\alpha }{\mathbf{s}}_{\kappa }^{\beta }>$ of the vortex line on both the one-dimensional wave vector $\kappa$ and intensity of the external force correlator $<{\zeta }_{\kappa }^{\alpha }{\zeta }_{\kappa }^{\alpha }>$ was studied. Here ${\mathbf{s}}_{\kappa }^{\alpha }$ is the Fourier transform of the line element position ${\mathbf{s}}^{\alpha }(\xi ,t)$. It is shown that under the influence of an external random force a vortex ring becomes a small tangle whose mean size depends on external force intensity. The theoretical predictions and the numerical results are in reasonable agreement.

latex, 7 pages, 2 Postscript figures, uses subeqnar.sty, sprmindx.sty, cropmark.sty, physprbb.sty, svmult.cls, to be published in "Quantized vortex dynamics and superfluid turbulence", Ed. C. Barenghi (Springer Verlag, Berlin, 2001)